Heat the oil in a medium cast-iron or other heavy-bottomed skillet over medium heat. Place the halved cabbage cut sides down in the pan. Just leave it to cook for 10 to 15 minutes, until the underside has become beautifully charred.
Lower the heat somewhat, add half of the butter, and shake the pan in order to spread the butter under and all around the cabbage. Once the butter has melted and begins to foam, tilt the pan toward you and spoon the butter over the cabbage, making sure to coat everything. Do this for half a minute, allowing the cabbage to cook further. As soon as the butter starts to brown, add another lump and repeat the process.
Stick a knitting needle or a steel skewer into the heart of the cabbage: Is it done yet? You should be able to pull out the skewer without effort. If not, allow the cabbage to tenderize some more. Douse with the fish sauce. Sprinkle the cabbage with the vinegar and season with salt (if needed) and pepper. Sprinkle with the tarragon and serve.
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